Computer simulations in physics by using characteristic examples 1101-5Eko11
The main goal of this lecture is to present typical, numerical methods for simulation and visualisation of some characteristic problems in classical and quantum mechanics as well as thermodynamics and statistical mechanics. For example,
1. Elements of statistical thermodynamics of small systems
2. Transport, diffusion and relaxation
3. Dynamic properties of polimers
4. Disordered systems: amorphous (glossy) and alloys
5. Phase transitions in magnetism
6. Elements of deterministic chaos
All the problems are considered by using concrete simulations (examples). The numerical metods are as follows:
A. Probabilistic methods
A1. Static "hit and miss" Monte Carlo method
A2. Dynamic Monte Carlo methods (Metropolis et al, Glauber) & Ising-Kawasaki kinetic
approach
A3. Monte Carlo renormalization group technique
A4. Quantum Monte Carlo methods
A5. Probabilistic cellular automata
B. Deterministic methods
B1. Molecular dynamics for solution of the ordinary differential equations
B2. Molecular dynamics for solution of the partial differential equations
B3. Eigenproblems in quantum mechanics
Prerequisites: Classical mechanics, quantum mechanics, thermodynamics, statistical physics
Examination: Examination
Mode
Self-reading
Prerequisites (description)
Course coordinators
Learning outcomes
After completion of the course the student obtained the following results in the field of education.
KNOWLEDGE
1) He knows the most important methods of statistical computer simulation of physical systems, mainly the basic Monte Carlo method based on Markov chain and process.
2) Knows basic `ab initio' deterministic methods of molecular dynamic simulations of physical systems.
SKILLS
1) He can formulate and represent the problems posed in the form of algorithmic.
2) He can independently design and carry out simulations of the effects, physical phenomena and processes of nature static and dynamic.
3) He can analyze and visualize (up-to-date in real time) the results of the computer simulations.
ATTITUDES
1) Appreciates the importance of a thorough and comprehensive understanding of the problem in drawing conclusions and making decisions.
It all corresponds to the following effects in the field of education (see information about studying at http://www.fuw.edu.pl/ ):
1) knowledge: KW01- KW06,
2) skills: KU05 - KU09,
3) competences: K04, K05.
EXPECTED STUDENT WORKLOAD:
- participation in classes (lectures 15h + exercises 15h): 30h - 1.0 ECTS,
- preparation for classes and the dissolution of homework: 30h - 1.0 ECTS,
- exam preparation: : 25h - 1.0 ECTS.
Assessment criteria
Completion of the course may be of two methods:
1) performance (in agreement with the lecturer) own design in the form of a computer simulation of the phenomenon or physical process,
2) by the traditional method in the form of a conversation.
Both methods require class attendance and active participation in them.
Practical placement
It is not expected
Bibliography
[1] D. Potter, Computational Physics, J. Wiley & Sons, London 1973 (transl. to Polish exists).
[2] T. Peng, An Introduction to Computational Physics, Cambridge Univ., Cambridge 1997 (transl. to Polish exists).
[3] S.E. Koonin, Computational Physics, Benjamin, Menlo Park 1986.
[4] D.P. Landau, K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics, Cambridge Univ. , Cambridge 2000.
[5] Monte Carlo methods in statistical physics, Topics in Current Physics, Vol.VII, red. K. Binder, Springer-Verlag, Berlin 1979.
[6] Applications of Monte Carlo methods in statistical Physics, Topics in Current Physics, Vol.36, red. K. Binder, Springer-Verlag, Berlin 1984.
[7] R.W. Hockney, J.W. Eastwood, Computer simulation using particles, McGraw-Hill, New York 1981.
[8] D. Dahlquist, A. Björck, Numerical Methods, Prentice-Hall, 1974 (tranl. to Polish exists).
[9] A. Krupowicz, Metody numeryczne zagadnień początkowych równań różniczkowych zwyczajnych, Państwowe Wydawnictwa Naukowe, Warszawa 1986.
[10] D. C. Rapaport, The art of molecular dynamics simulation, Cambridge University Press 1998.
[11] R. Kutner, Elementy mechaniki numerycznej z oprogramowaniem komputerowym, WSiP, Warszawa 1991.
[12] R. Kutner, Elementy fizyki statystycznej w programach komputerowych. Cz.I. Podstawy probabilistyczne, WSiP, Warszawa 1991.
[13] J. Ginter, R. Kutner, Komputerem w kosmos, WSiP, Warszawa 1990.
[14] Fizyka i astronomia dla liceum ogólnokształcacego, liceum profilowanego i technikum. Kształcenie ogólne w zakresie podstawowym (wraz z oprogramowanien na CD), Nowa Era, Warszawa 2005.
[14] D. C. Rapaport, The art of molecular dynamics simulation, Cambridge University Press 1998.
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: